Thread: Finding the equation for a plane

The plane that contains the points (8,3,1), (2,6,3), and (4,6,2) has an equation of the form ax+by+cz=d. Find coefficients fr this equation, trying two different approaches to the problem. One method uses vectors, another does not.

Since the points lie in the plane, the vectors and
are parallel to the plane.

The cross product:


is normal to the plane.

Use this normal and the point (8,3,1):



And we get:





Now, try the other method.